ch1_add_2 - Additional Examples of sample spaces and events...

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Additional Examples of sample spaces and events Example 1: In the experiment of tossing a single regular six-sided die, there are six possible outcomes. Thus the sample space is Ω={ , , , , , }. This may also be depicted simply as Ω={ 1, 2, 3, 4, 5, 6}. Let A be the event that even number of spots turn up, i.e. A ={ , , }. Or A={2,4,6}. A is an event; that is it consists of a subset of elementary outcomes in Ω. Since in this example the sample space is finite, the event space, sometimes denoted by A. , consists of all subsets of Ω. Thus, there are 6 2 =64 events, of which only 6 are elementary, in A. , including both φ and Ω. Example 2: Toss a penny, nickel, and a dime simultaneously, not whether heads (H) or tails (T ) is up. There are eight possible outcomes of this experiment; thus Ω={(H,H,H), (H,H,T), (H,T,H), (T,H,H), (H,T,T), (T,H,T),(T,T,H), (T,T,T)}. We are using the first posi tion of the 3-tuple (∙,∙,∙) to record the outcome of the penny, the second position to record
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